Two best friends with Down Syndrome are ecstatic to discover that they have been selected to test Hoogle’s new technology: the Hoogle Hat. But when the hat seems to brainwash the other test subjects, they realize that they are the only people who can stop Hoogle from taking over the world.

Best to avoid unnecessary lengthy descriptions and overly wordy sentences in a logline. Get strait to the plot i.e:
A significant event happens to a main character, with a specific flaw, that must take action to achieve a clear objective goal.

How about this?

Two best friends with Down Syndrome learn they've been selected to participate in a controversial project that increases intelligence. But when the friends uncover that the doctor running the program is brainwashing his other test subjects, they must team-up using their new found intelligence to stop the doctor from enslaving the masses. Something like that.

You could explain the Hoogle Hat and who Dr. Hoogle is in your synopsis.

Hope this helps.

Okay very helpful again. How about this:

When a depressed young man with Down Syndrome meets someone online looking for subjects to test his ?cure? on, he enlists the help of his best friend to travel to Florida with the hopes of finding a cure.